3D trajectory analysis of a single ceria particle with confined motion near a glass surface

We demonstrate here an expeditious method for obtaining 3D trajectories of single ceria particles at three different pH values using data obtained from EW microscopy coupled with video imaging (Fig. 2). Positions (i.e., centroids) of single ceria particles near a glass surface in each frame were identified from local maxima in their EW scattering intensity fitted to a Gaussian function using the particle tracking software [Reference Vallotton, Van Oijen, Whitchurch, Gelfand, Yeo, Tsiavaliaris, Heinrich, Dultz, Weis and Grünwald17]. 2D trajectories of a single ceria particle were obtained by linking its time-sequenced positions (upper figure in Fig. 2). The distance of the particle from the glass surface in the z-direction (height, h) can be obtained using the Beer–Lambert relation between h and the EW intensity (lower figure in Fig. 2), h(I) = β ln(I ₀/I) [Reference Prieve18,Reference Prieve and Walz19], where β (88.0 ± 4.5 nm) is the penetration depth of the laser beam, I is the EW scattering intensity of the ceria particle, and I ₀ is the maximum intensity obtained at the particle/surface interface [Reference Prieve18]. EW intensity is maximum at the glass surface and decays exponentially with the distance h according to I(h) = I ₀ exp(–β⁻¹h) [Reference Prieve18,Reference Prieve and Walz19]. The penetration depth β is defined as the distance from the glass surface where EW intensity decays to 1/e or ~37% of I ₀ [Reference Prieve18,Reference Prieve and Walz19]. It should be noted that the imaging depth is not limited to the penetration depth and particles located beyond the EW penetration depth from the glass surface can also be imaged [Reference Prieve and Walz19,Reference Liu, Woolf, Rodriguez and Capasso20,Reference McKee, Clark, Walz and Ducker21,Reference Hertlein, Riefler, Eremina, Wriedt, Eremin, Helden and Bechinger22,Reference Gell, Berndt, Enderlein and Diez23]. For example, Prieve and Walz reported smaller than 400 nm separation distance using a 7 μm polystyrene sphere with a penetration depth of 197 nm [Reference Prieve and Walz19]. McKee et al. calibrated the relationship between EW intensity and particle–surface distance and showed that the effective range of separation distance using a 1.2 μm glass particle and a penetration depth of 66.8 nm was about three times the penetration depth [Reference McKee, Clark, Walz and Ducker21]. The separation distances h of ceria particles near a glass surface, obtained from the intensity data in our paper, are less than ~3 times the penetration depth and thus can be used as the distance h for their 3D positions. 3D positions of the particles were determined by combining 2D positions with the associated separation distance h in each frame, and then linking them to generate 3D trajectories (Fig. 2).

Figure 2: Trajectory of a single ceria particle near a glass surface in 2D (x–y) plane (upper figure where each colored track shows the particle's movement between two different frames). EW intensity of a single particle versus time data is shown in the lower figure. The 3D trajectory of a single ceria particle was obtained by combining the 2D (x–y) data with the separation distance h (see the next section for details). The first and last three points of the 3D trajectory were marked as black dots to determine the beginning and the end of the particle movement.

50 μL of a dilute ceria suspension was placed on the flat surface of the glass lens and imaged in situ using EW microscopy for 20 s. The number of ceria particles on the glass surface, obtained from EW microscopy images and videos, is ~2950 at pH 3, ~1530 at pH 5, and ~427 at pH 7 in the imaged area of 77 × 77 μm², corresponding to ~0.5, ~0.3, and ~0.1 particles/μm², respectively. Thus, the concentrations of the ceria particles on the glass surface are sufficiently low, so that particle–particle interactions are negligible. Indeed, to minimize the effect of particle–particle interactions in our analysis, only particles that were more than 10 particle diameters apart from neighboring particles were monitored. For trajectory analysis, three different single ceria particles each at three different pH values were monitored as representative samples. Figure 3 shows representative 3D and 2D trajectories of one of these three ceria particles, tracked for 500 frames over a total time of 20 s, at pH 3, 5, and 7. These data were obtained from separate experiments performed at each pH value and combined into a single figure. In Fig. 3, the time evolution of these positions can be visualized from the color scheme that changes gradually from red initially (t = 0) to blue at t = 20 s.

Figure 3: 3D trajectories of three different single ceria particles near a glass surface at pH 3, 5, and 7. These data were obtained from individual experiments performed at three different pH values and combined into a single figure.

The movements of single ceria particles at pH 3 and 5 are confined to a relatively small area of 15 × 15 nm² and 30 × 30 nm², respectively, due to strong attractive electrostatic and van der Waals forces (zeta-potentials of ceria particle at pH 3 and 5 are 70 and 50 mV, respectively, and that of SiO₂ film is −20.0 mV) [Reference Seo, Gowda, Khajornrungruang, Hamada, Song and Babu12]. The isoelectric point (pH_IEP) of the glass (SiO₂) film is 2.0, resulting in a negatively charged glass surface in the pH range we are interested in. The vertical separation distance h, obtained from the intensity data, showed that the particles were also confined in the z-direction over a height of about 15 and 45 nm at pH 3 and 5, respectively. By contrast, the movements of single ceria particles near the glass surface at pH 7, though still confined, covered an area of 300 × 300 nm² and a vertical distance along a z-axis of 150 nm, presumably due to the consequence of the weaker attractive forces between the ceria particle and the glass surface (zeta-potential of ceria particle at pH 7 is close to 0 mV and that of SiO₂ film is −34.0 mV) [Reference Seo, Gowda, Khajornrungruang, Hamada, Song and Babu12]. Different types and characteristics of particle motions observed at pH 7 will be discussed in the subsequent section. The increases seen in the space covered by the particles with pH corroborate the findings from potential energy curves that showed that the separation distance increases with pH due to weakening of the attractive forces at higher pH values [Reference Seo, Gowda, Khajornrungruang, Hamada, Song and Babu12].

Mean square displacement (MSD) of any particle along its trajectory can be obtained at various lag times τ_n (τ_n = nΔt, n = 1, 2, … N − 1) using the definition [Reference Huang, Watson, Dempsey, Suh, Weissig, Elbayoumi and Olsen24,Reference Jeon, Leijnse, Oddershede and Metzler25]

$$ \! {\rm MS}{\rm D}_{3{\rm D}} \! = \displaystyle{1 \over {N-n}}\sum\limits_{i = 0}^{N-n} {\lpar {\lpar x_{i + n}-x_i\rpar }^2 + {\lpar y_{i + n}-y_i\rpar }^2 + {\lpar z_{i + n}-z_i\rpar }^2\rpar },$$

where N is the total number of time frames (N = 500) over which the trajectories were imaged, Δt is the time interval between two consecutive image frames (40 ms in our case) defined by the frame acquisition rate, and n is the number of the time intervals. Also, (x _i+n, y _i+n, and z _i+n) are the positions of the particle at time nΔt after starting at position (x_i, y _i, and z_i) at t = 0. Again, at any time, the particle positions are given by those of its centroid where the highest intensity occurs, determined by fitting a Gaussian profile using the Diatrack software as described in the Experimental section.

Figure 4 shows the MSD_3D curves at three different pH values. MSD_3D of single ceria particles at pH 3, 5, and 7 increased with increasing τ, and this trend is similar to that observed in the case of 2D data [Reference Seo, Gowda, Khajornrungruang, Hamada, Song and Babu12]. If a particle shows anomalous diffusion, its MSD_3D exhibits a nonlinear relationship with τ, expressed by a power law of the form MSD_3D = 6D _3Dτ^a where D _3D is three-dimensional diffusion coefficient and a is the exponent that determines the types and characteristics of particle motions [Reference Ben-Avraham and Havlin26,Reference Havlin and Ben-Avraham27,Reference Höfling and Franosch28]. If 0 < a < 1, the motion is said to be confined or sub-diffusive, Brownian if a = 1, and super-diffusive if a > 1 [Reference Ben-Avraham and Havlin26,Reference Havlin and Ben-Avraham27,Reference Höfling and Franosch28]. In our case, the value of the exponent a obtained by fitting the data is ~0.11 for pH 3 and 5 and ~0.14 for pH 7 confirming confined motion of the particle. The associated three-dimensional diffusion coefficients D _3D are 1.4 × 10⁻⁵, 6.7 × 10⁻⁵, and 1.0 × 10⁻³ μm²/s, at pH values of 3, 5, and 7, respectively. These D _3D values are the mean values of the diffusion coefficients of three different single particles calculated for the same experimental conditions. The calculated values of D _3D increase significantly with increasing pH, with the D _3D at pH 7 being roughly 70 times higher than that at pH 3, reflecting the weaker attractive interaction forces between the particles and the glass surface at the higher pH.

Figure 4: Mean square displacement, MSD_3D as a function of lag time τ. (a) log–log plots and (b) linear–linear plots. The data were fitted to MSD_3D = 6D _3Dτ^a, where D _3D is the three-dimensional diffusion coefficient. The exponent a was found to be 0.11, 0.11, and 0.14 for the three different pH values of 3, 5, and 7, respectively. The shaded regions around each line indicate the ranges for MSD determined from the data on three different particles.

Two types of 3D trajectories of single ceria particles, one with confined and one with Brownian motion, and a third type of an agglomerated cluster, all at pH 7

Two entirely different particle motions of single ceria particles in 2D (x–y) plane were observed at pH 7 [Reference Seo, Gowda, Khajornrungruang, Hamada, Song and Babu12]. As explained above, the motion of particle 1 was similar to the confined motion that was observed at pH 3 and 5. In the second case (particle 2), the particle moved rapidly and moved far away from the glass surface and sometimes disappeared from the field of view. Therefore, the second particle could be tracked for a time period of only 5 s which yielded a sequence consisting of only 125 images that covered the space between ~−1500 and ~1500 nm in the x- and y-directions and between ~5 and ~270 nm in the z-direction [Fig. 5(a)]. In contrast, the particle showing confined motion could be tracked for the complete 20 s since it moved in a much smaller area of 300 × 300 nm² and smaller vertical distance along a z-axis of 150 nm (Fig. 3). Analysis of the MSD_3D [Fig. 5(c)] of the second particle showed that it is undergoing Brownian motion since the exponent a is ~1, while the first particle is undergoing confined motion since a is 0.14 as shown in Fig. 4. This difference is a consequence of the zeta-potential of ceria particles at pH 7 being close to 0 mV [Reference Seo, Gowda, Khajornrungruang, Hamada, Song and Babu12]. This means that while both positive and negative charges exist on the particle surface at the same time in different regions, they counterbalance each other. Several authors reported the non-uniform distribution of zeta-potential on the particle surface and their standard deviation among different regions [Reference Velegol, Feick and Collins29,Reference Feick and Velegol30,Reference Velegol and Thwar31]. In our case, if it so happens that the attractive interaction of the positively charged parts on the surface of a specific particle with the negatively charged glass surface is dominant, then it results in confined motion. If either the local repulsion induced by the negative charge on the particle surface or the weakened attraction due to the net value of the zeta-potential being close to zero is dominant, then the particle can move further away from the glass surface resulting in Brownian motion. In such a case, the weakened interaction allows the particle to move farther and faster from the glass surface as seen in our measurements. As such, the particle with Brownian motion can move ~270 nm away from the glass surface, while the particle with confined motion can only move up to ~150 nm.

Figure 5: 3D trajectories of (a) single ceria particle with Brownian motion and (b) agglomerated cluster and single ceria particle with confined motion all at pH 7 and (c) the corresponding MSD_3D data as a function of τ; log–log plots and linear–linear plots. The exponent a for MSD_3D for single ceria particle with Brownian motion (red) and an agglomerated cluster (black) are 1.05 and 0.22, respectively. 3D trajectory of the single particle with confined motion is the same as that shown in Fig. 3.

Additionally, since the zeta-potential of ceria particle at pH 7 is close to 0 mV, particle agglomeration occurs. Agglomeration of particles in colloidal dispersions is well known and occurs when the zeta-potential is very low and is caused by the dominance of van der Waals attraction [Reference Seo, Gowda, Khajornrungruang, Hamada, Song and Babu12,Reference Seo, Paik and Babu32,Reference Sigmund, Bell and Bergström33]. Among many agglomerated clusters observed in the imaged area, one such agglomerated cluster (particle 3) was chosen as a representative sample. The 2D trajectory of the agglomerated cluster (particle 3) was obtained by tracking local highest EW scattering intensity (closest to the glass surface) of the cluster and fitting it to a Gaussian function using the particle tracking software [Reference Vallotton, Van Oijen, Whitchurch, Gelfand, Yeo, Tsiavaliaris, Heinrich, Dultz, Weis and Grünwald17] and then combined with the distance of the agglomerated cluster from the glass surface in the z-direction to generate its 3D trajectory [Fig. 5(b)]. Analysis of the MSD_3D of this cluster showed that it is undergoing confined motion since a is ~0.2 [Fig. 5(c)].

The D _3D of the single particle undergoing Brownian motion (2.0 × 10⁻¹ μm²/s) is about 200 times higher than that of the particle with confined motion (1.0 × 10⁻³ μm²/s). The D _3D of the agglomerated cluster (8.8 × 10⁻⁴ μm²/s) is only slightly lower than that of the particle with the confined motion, perhaps because of the gravitational attraction. The D _3D values are summarized in Table 1 along with the D _2D values that were calculated earlier from MSD_2D curves (MSD = 4D _2Dτ^a) [Reference Seo, Gowda, Khajornrungruang, Hamada, Song and Babu12]. The D _3D of the single ceria particles at pH 3, 5, and 7 and of the agglomerated clusters at pH 7 showing confined motion were slightly lower than their D _2D (Table 1), presumably due to the attractive interaction forces along the z-directions.

TABLE 1: Summary of D _2D and D _3D of ceria particles near a glass surface at pH 3, 5, and 7 obtained from their respective MSD data as a function of lag time τ. D _2D values are from our previous paper [Reference Seo, Gowda, Khajornrungruang, Hamada, Song and Babu12].

The bulk diffusion coefficient (D ₀) of the ceria particles obtained from dynamic laser scattering (DLS) measurements based on the Stokes–Einstein equation has a value of 3.0 μm²/s [Reference Seo, Gowda, Khajornrungruang, Hamada, Song and Babu12], but the D _3D of even the particle exhibiting Brownian motion at pH 7 calculated from MSD_3D is only 0.2 μm²/s [Fig. 5(c)], a value that is 15 times smaller. The diffusion coefficients along x-, y-, and z-directions of a particle undergoing Brownian motion used in DLS experiments are the same, Dx = Dy = Dz, due to the homogeneous environment. Also, the equation used to calculate diffusion coefficients using DLS does not consider any external forces (e.g., repulsive or attractive forces) acting on a particle. However, our system here is aimed at studying particle–surface interactions that influence particle motion, and the much lower D _3D values obtained from our experiments as compared to D ₀ are likely due to the electrostatic attractive forces prevailing between ceria particles and glass surface.

In the next section, we will discuss how the pH-dependent 3D trajectories, three-dimensional diffusion coefficients, and interaction potential energy data (obtained in our previous paper [Reference Seo, Gowda, Khajornrungruang, Hamada, Song and Babu12]) of ceria particles near a glass surface are related to their removal by repeated washing with DI water adjusted to pH 10 and 12.

Removal of ceria particles from a glass substrate as a function of the number of washes at pH 10 and 12

Ceria particle-based slurries have been widely used for SiO₂ polishing, especially for shallow trench isolation (STI) chemical mechanical planarization (CMP) because of their high chemical affinity toward SiO₂ films [Reference Srinivasan, Dandu and Babu34]. However, this affinity presents a major challenge for post-CMP cleaning as the particles strongly adhere to the wafer surface during polishing [Reference Seo, Gowda and Babu5,Reference Gowda, Seo, Ranaweera and Babu35]. With device dimensions, now at 7 nm, continuing to shrink, there is a strong need to understand various chemical and mechanical phenomena that occur in the brush cleaning systems used to remove these particles. Here, we show the relationship between 3D trajectories, three-dimensional diffusion coefficients, and interaction potential energy data of ceria particles and particle cleaning using pH-adjusted de-ionized water (DIW), as imaged by EW spectroscopy. While the actual post-CMP cleaning of oxide surfaces is a very complex engineering process, the results obtained here provide valuable insights. As stated earlier, the flat glass surface of the lens became our model for the SiO₂ film surface of interest here.

50 μL of a ceria slurry was placed on the glass surface and imaged after 20 min. Figure 6 displays the EW images of ceria particles left on the glass surface (covering an area of 77 × 77 μm²) at pH 3, 5, and 7 and cleaned for 40 s using a water jet from a simple spray bottle containing DIW adjusted to pH 10 and 12 and then imaged as a function of the number of washes. The higher pH values were chosen for cleaning to benefit from the repulsive forces at these values between ceria particles and glass surfaces. The number of ceria particles initially present on the glass surface decreased with an increase in pH (~2950 at pH 3, ~1530 at pH 5, and ~427 at pH 7). After cleaning, the number of residual ceria particles on the glass surface was determined as a function of the number of washes at both pH 10 and 12 (Fig. 7). The corresponding cleaning efficiencies, defined as the number of particles remaining as a percent of the particles initially present, are summarized in the inset in Fig. 7.

Figure 6: EW microscopy images of ceria particles adsorbed at (a) pH 3, (b) pH 5, (c) pH 7 and their removal using DIW adjusted to pH 10 and 12 as a function of number of washes. The first image in each row was captured 20 min after placing the sample on the lens. The subsequent images were obtained after washing the particles from the lens. The first and second rows in each panel display the EW scattering images of residual ceria particles after washing with DIW adjusted to pH 10 and 12, respectively. N is the number of ceria particles on the glass surface.

Figure 7: Number of ceria particles calculated from EW microscopy images shown in Fig. 6 at (a) pH 3, (b) pH 5, and (c) pH 7 and their removal as a function of the number of washes using DIW adjusted to pH 10 (filled symbols) and pH 12 (open symbols). Inset shows the corresponding cleaning efficiencies.

Cleaning efficiencies of DIW adjusted to pH 10 and 12 for removal of ceria particles from the samples prepared at pH 3 reached 88% and 99% [Fig. 6(a)], respectively, after 8 washes. In contrast, particles on the samples prepared at pH 5 [Fig. 6(b)] and pH 7 [Fig. 6(c)] can be cleaned with higher efficiencies at both pH 10 and 12 after only 3 or 4 washes. These results are consistent with the above 3D trajectory data and the measured interaction potential energy data [Reference Seo, Gowda, Khajornrungruang, Hamada, Song and Babu12] that showed that ceria particles at pH 3 can remain closer to the glass surface making them more difficult to be cleaned when compared to particles at pH 5 and 7 which can move farther and faster from the glass surface due to the weakening of the attractive forces [Reference Seo, Gowda, Khajornrungruang, Hamada, Song and Babu12]. Earlier, we demonstrated the ceria particles adsorbed on oxide surfaces via strong Ce–O–Si bond could not be removed effectively by only charge repulsion [Reference Seo, Gowda and Babu5]. pH-adjusted DIW (pH 13.5) showed negligible cleaning efficiency (<5%) for 90 nm ceria particles, even when aided by ultrasonic cleaning [Reference Seo, Gowda and Babu5]. In this study, ceria particles move near the glass surface at pH 3, 5, and 7 without the formation of strong Ce–O–Si bonds with the glass surface, and hence DIW adjusted to pH 10 and 12 was able to remove them from the surface by only charge repulsion. While charge repulsion is known to be a key driver of cleaning performance, our data provide a quantitative measure of this effect. This is especially true for the larger particles used here since we recently showed that smaller (sub-50 nm) ceria particles with a higher surface concentration of Ce³⁺ adsorbed on oxide surfaces cannot be removed effectively by only charge repulsion because they are more strongly coupled with oxide surfaces via strong Ce–O–Si bonds [Reference Seo, Gowda and Babu5]. Such smaller particles can be removed only after breaking this bond and not by just relying on electrostatic repulsion [Reference Seo, Gowda and Babu5].

3D versus 2D data analysis and results

One can argue that the calculation of MSD of particles traveled in 3D, and the 3D diffusion coefficients did not provide any new insights beyond those obtained from a 2D analysis. However, this in itself is remarkable since we would not have predicted it beforehand and may not apply to all systems. We find, for example, that while particles are easily removed during cleaning, significant particle redeposition occurs and prevents complete particle removal using a rotating PVA brush, a common practice in the industry to clean wafers post-CMP. Particle redeposition is determined by the diffusion and/or convective transport in the thin liquid film, where the 3D trajectories and diffusion coefficients matter, between the glass and the porous PVA brush surfaces. These processes are being imaged and analyzed now using EW spectroscopy [Reference Terayama, Khajornrungruang, Suzuki, Kusatsu, Hamada, Wada and Hiyama16].

Furthermore, using our extended methodology and based on the techniques developed to study brush cleaning, it should be possible to image pad/wafer and pad/abrasive (ceria or silica)/wafer contact during polishing—something that has not been possible so far—using model wafer coupons and polishing pad pieces. Finally, one might be able to investigate the behavior of smaller ceria and other particles using only 2D data since gravitational effects will be lower.